China, not the CCP. They view themselves as the rightful leadership party.
This is very historical though. When polled on whether Taiwan would want to become part of China, remain independent, or become part of the US (!), the majority wants US Statehood.
I'll go look up sources and cite them in just a bit.
Yep, at the end of the day the whole fiasco between Taiwan and the PRC isn't really about Taiwan. It's about US-PRC relations and who gets the final word in Asia. Taiwan is just a game piece.